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Number of acyclic digraphs on n unlabeled nodes with a global source (or sink).
10

%I #14 Jan 09 2022 12:44:11

%S 1,1,3,16,164,3341,138101,11578037,1961162564,668678055847,

%T 457751797355605,628137837068751147,1726130748679532455689,

%U 9493834992383031007906911,104476428350838383854529661007,2299979227717819421763629684068904

%N Number of acyclic digraphs on n unlabeled nodes with a global source (or sink).

%C A local source (also called an out-node) is a node whose in-degree is zero. In the case of an acyclic digraph with only one local source, the source is also a global source.

%H Andrew Howroyd, <a href="/A350415/b350415.txt">Table of n, a(n) for n = 1..50</a>

%H Marcel et al., <a href="https://mathoverflow.net/q/395095">Is there a formula for the number of st-dags (DAG with 1 source and 1 sink) with n vertices?</a>, MathOverflow, 2021.

%o (PARI) A350415seq(16) \\ See PARI link in A122078 for program code.

%Y The labeled case is A003025.

%Y Row sums of A350488.

%Y A diagonal of A122078.

%Y Cf. A003087, A345258, A350360.

%K nonn

%O 1,3

%A _Andrew Howroyd_, Dec 29 2021